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Diana: A Mathematica Code for Making Dimensional Analysis

R. M. Muradian
Alexander L. Urintsev
Organization: Joint Institute for Nuclear Research
Department: Laboratory of Particle Physics
Journal / Anthology

Byurakan Astrophysical Observatory, Armenia
Year: 1994
Volume: E2-94-110
Page range: 1-24

Mathematica is one of the newest and most powerful computer systems for doing symbolic, numerical, graphics, and programming manipulations. With its large capabilities, Mathematica opens new prospects for solving a broad range of problems in physics, engineering and economics. The Mathematica package Diana was designed and implemented by us for making automatic and quick dimensional analysis for any problem in physics and engineering. The package is based on the fundamental principles of dimensional analysis formulated in the matrix form. Materials from other common textbooks and articles on dimensional analysis are used. A comprehensive treatment of the modern state of art together with the thorough list of the literature can be found. The basic principles of dimensional analysis are realized by using capabilities provided by the Mathematica's function LinearSolve and NullSpace. It is proposed to increase the number of the SI base units by addition of the new fundamental unit of price -- dollar $ -- for solving financial problems in engineering physics.

*Applied Mathematics